Geometry and mechanics of knitted fabric

Knitted fabric consists of yarn that is stitched together in a repeated pattern. The fabric is held together by internal stresses due to the large contortions of its threads, which are linked together in slipknots, placing physical constraints on thread displacement. The result is a material with extremely soft bending elasticity that is also able to stretch. Due to the complex structure of knitted fabrics, much is unknown about the collective mechanics of these materials and there is not currently an accurate constitutive model. As such, modeling is limited to computationally-intensive yarn-level simulations. Additionally, global properties of the fabric are sensitive to the local geometry of the stitches. The intrinsic asymmetry between the front and the back of stitches yields a fabric that has the propensity to curl, rather than lay flat. We seek a set of constitutive relations for a variety of stitch patterns by examining the equilibrium stress distribution in a model of linked elastica, with the ultimate goal of developing a robust continuum theory. Our results provide a guide to developing fabrics with intrinsic geometry and mechanics that are controlled by stitch pattern, as well as allowing for fast and accurate simulations for CGI films and video games.